document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=495284>Question 495284</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have 8 runners in a race...what is the probability that i will pick 1, 2 and 3rd place </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #336055 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=336055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the probability you will pick the winner is 1/8<BR>\n" );
document.write( "if you are so lucky to pick the winner, the probability you will pick second place runner is 1/7.<BR>\n" );
document.write( "if you are so lucky to pick second place, the probability you will pick third place is 1/6.<BR>\n" );
document.write( "the probability you will pick all 3 is 1/8 * 1/7 * 1/6 = 1/336.<BR>\n" );
document.write( "you might be able to see this easier if we had only 3 runners and we had to pick the first and second place finish.<BR>\n" );
document.write( "assume the runners are a, b, and c<BR>\n" );
document.write( "the probability you will pick the winner is 1 out of 3.<BR>\n" );
document.write( "the possible finishes are:<BR>\n" );
document.write( "abc<BR>\n" );
document.write( "acb<BR>\n" );
document.write( "bac<BR>\n" );
document.write( "bca<BR>\n" );
document.write( "cab<BR>\n" );
document.write( "cba<BR>\n" );
document.write( "you can see that:<BR>\n" );
document.write( "a finishes first in 2 out of the 6 possible permutations.<BR>\n" );
document.write( "b finishes first in 2 out of the 6 possible permutations.<BR>\n" );
document.write( "c finishes first in 2 out of the 6 possible permutations.<BR>\n" );
document.write( "the probability of any one of them finishing first is 2 out of 6 which is equal to 1/3.<BR>\n" );
document.write( "now, suppose you picked a, and a was in first place.<BR>\n" );
document.write( "that leave b and c to finish second or third.<BR>\n" );
document.write( "the possible permutations are now:<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "cb<BR>\n" );
document.write( "that means that:<BR>\n" );
document.write( "b finishes second in 1 out of the 3 possible permutations.<BR>\n" );
document.write( "c finishes second in 1 out of the 3 possible permutations.<BR>\n" );
document.write( "the probability of any one of them finishing second is 1 out of 2 which is equal to 1/2.<BR>\n" );
document.write( "the probability of both occurrences happening is 1/3 * 1/2 = 1/6.<BR>\n" );
document.write( "look at all 6 possible permutations again.<BR>\n" );
document.write( "abc<BR>\n" );
document.write( "acb<BR>\n" );
document.write( "bac<BR>\n" );
document.write( "bca<BR>\n" );
document.write( "cab<BR>\n" );
document.write( "cba<BR>\n" );
document.write( "you pick a to be the winner and b to be second.<BR>\n" );
document.write( "a is the winner and b is second in only 1 out of the 6 possible permutations.<BR>\n" );
document.write( "that's your answer.<BR>\n" );
document.write( "the probability is 1 out of 6.<BR>\n" );
document.write( "in your problem, the number of runners is 8 and you are trying to pick the first 3 winners.<BR>\n" );
document.write( "p(first) is 1/8<BR>\n" );
document.write( "p(second) is 1/7<BR>\n" );
document.write( "p(third) is 1/6<BR>\n" );
document.write( "p(all three) is 1/8 * 1/7 * 1/6 = 1/336<BR>\n" );
document.write( "same thing only more runners to choose from so it's a lot harder to show you how it  works.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );